Breakthrough Asymmetries across Disciplines and Countries: A Network approach to Structural Complexity of Scientific Progress

Abstract

Science is driven by community endeavors across diverse fields and specializations, forming a complex structure that renders conventional performance evaluation methods inadequate. Using established indicators, the network-based normalized citation score, and the disruptive index, combined with the GENEPY algorithm, we evaluate the complexity rank of countries based on their breakthrough performance across 89 subfields of physical sciences, drawing on nearly 60 million articles (1900-2023). This quality-focused integrated approach reveals pronounced asymmetries: while countries such as the United States, Israel, and several in Europe sustain long-term structural advantages, emerging nations show rapid gains in later decades. A power-law relationship between aggregated breakthrough performance and countries' R&D expenditure underscores the unequal and scale-dependent nature of global science. These results demonstrate that scientific advancement arises not from uniform growth but from asymmetric complexity, offering actionable insights for policymakers and funding agencies aiming to foster sustainable, high-quality research ecosystems.